Suppose that G11 is alive. Black to live in the best way with the top group.
(;SZ[19]AW[da]AW[ha]AW[db]AW[hb]AW[dc]AW[hc]AW[jc]AW[dd]AW[hd]AW[de]AW[ge]AW[df]AW[gf]AW[dg]AW[ig]AW[ei]AB[ea]AB[ga]AB[eb]AB[gb]AB[ec]AB[gc]AB[ed]AB[gd]AB[if]AB[fh]AB[gi]GM[1]FF[4]CA[UTF-8]AP[CGoban:2]ST[2]RU[Japanese]KM[0.00]PW[white]PB[black]
(;B[fb];W[fd]
(;B[fe];W[ee];B[ff];W[fg])
(;B[ee];W[fe]C[can't connect];B[ef];W[eg]C[can't connect]))
(;B[fd];W[fb]C[can't connect])
(;B[fe]
(;W[ee]C[CHOICE]
(;B[ff];W[fg]
(;B[gg];W[eg]
(;B[he]C[RIGHT])
(;B[fd];W[he]C[you could do better in this variation]))
(;B[fd];W[eg]C[you could do better in this variation])
(;B[eg];W[gg]C[black is dead]))
(;B[fd];W[ff]C[you could do better in this variation])
(;B[fb];W[fd];B[ff];W[fg]))
(;W[ff]C[CHOICE]
(;B[fb];W[ee];B[fd]C[alive, but lost some points])
(;B[ee]C[RIGHT])
(;B[ef];W[ee]C[oops, you died])))
(;B[ee];W[fe]
(;B[ef];W[eg]
(;B[fg];W[ff];B[he];W[hf];B[ie];W[hg]C[white wins])
(;B[fd];W[fb]C[you're removing your own liberties])
(;B[fb];W[fd]C[you're removing your own liberties])
(;B[ff];W[fg]C[dead]))
(;B[fd];W[fb];B[ef];W[eg]C[can't connect])
(;B[fb];W[fd];B[ef];W[eg]C[can't connect]))
(;B[he];W[fe])
(;B[ff];W[fe])
(;B[ef];W[ee]))